A110640 -id:A110640 - cp's OEIS frontend

A112573 G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9.

1, 1, 0, 0, 2, -2, 5, -6, 5, 3, -26, 70, -141, 221, -229, -18, 891, -2914, 6524, -11238, 13690, -4214, -37619, 145018, -353534, 657080, -895234, 534007, 1654246, -7840402, 20737566, -41200153, 61402057, -50500722, -68352913, 441195837, -1272153666, 2690651374

Offset: 0

Paul D. Hanna, Sep 14 2005

sign

A110640 is formed from every third term of A083949, which also consists entirely of numbers 1 through 9.

			A(x) = 1 + x + 2*x^4 - 2*x^5 + 5*x^6 - 6*x^7 + 5*x^8 + 3*x^9 +...
A(x)^3 = 1 + 3*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 9*x^6 + 6*x^7 +...
A(x)^9 = 1 + 9*x + 36*x^2 + 84*x^3 + 144*x^4 + 252*x^5 + 489*x^6 +..
A(x)^9 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6+..
G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 + 9*x^7 +...
where G(x) is the g.f. of A083949.

Cf. A110640, A083949.

{a(n)=local(d=3,m=9,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break))); polcoeff(Ser(vector(n+1,i,polcoeff(A,d*(i-1))))^(1/3),n)}

G.f. A(x) satisfies: A(x)^9 (mod 27) = g.f. of A083949.

A110639 Every 9th term of A083949 where the self-convolution 9th power is congruent modulo 27 to A083949, which consists entirely of numbers 1 through 9.

Original entry on oeis.org

1, 1, 9, 9, 2, 7, 5, 3, 5, 3, 1, 7, 3, 5, 5, 9, 9, 2, 8, 3, 1, 7, 1, 1, 4, 8, 5, 1, 1, 2, 9, 2, 7, 6, 8, 6, 6, 7, 2, 2, 5, 6, 5, 9, 6, 1, 6, 7, 4, 5, 6, 4, 9, 8, 4, 1, 4, 9, 9, 2, 3, 1, 9, 4, 2, 6, 6, 8, 2, 5, 3, 2, 5, 2, 8, 2, 4, 6, 4, 8, 6, 2, 5, 2, 8, 9, 8, 1, 2, 3, 3, 2, 9, 1, 1, 1, 4, 8, 5, 5, 7, 8, 7, 3, 1

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

nonn

			A(x) = 1 + x + 9*x^2 + 9*x^3 + 2*x^4 + 7*x^5 + 5*x^6 +...
A(x)^9 = 1 + 9*x + 117*x^2 + 813*x^3 + 5976*x^4 + 33381*x^5 +...
A(x)^9 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 +...
G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 +...
where G(x) is the g.f. of A083949.

Cf. A083949, A110640, A110641.

{a(n)=local(d=9,m=9,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}

cp's OEIS Frontend

A112573 G.f. A(x) satisfies: A(x)^3 equals the g.f. of A110640, which consists entirely of numbers 1 through 9.

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